ACT Math Practice Question #1281 (Medium (31)) | Test Citadel
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ACT Math Difficulty: Medium (31)

Digital ACT Math Practice Question #1281

Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.

What is the domain of the real-valued function $f(x) = \frac{\sqrt{4x - 12}}{x - 7}$?
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Socratic AI Engine Step-by-Step Derivation
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⚡ 15-Second Desmos Speed Hack

Check boundaries: $x = 3 \implies \sqrt{0}/(-4) = 0$ (valid, eliminates strict inequality). $x = 7 \implies$ division by zero (must be excluded). Instantly identifies $x \ge 3$ and $x \ne 7$.

Masterclass Solution & Distractor Trap Analysis

For $f(x)$ to be real-valued, two conditions must hold simultaneously: 1. The radicand under the square root must be nonnegative: $4x - 12 \ge 0 \implies 4x \ge 12 \implies x \ge 3$. 2. The denominator cannot be zero: $x - 7 \ne 0 \implies ...

Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...

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